A current issue for a color adjustable light emitting diode (LED) light source is color rendering properties. To obtain a sufficiently large color gamut, the light source normally comprises three color LEDs: red, green, and blue. This is described in U.S. Pat. No. 6,411,046, where light output and the color of the LEDs are controlled by measuring color coordinates for each LED light source for different temperatures, storing the expressions of the color coordinates as a function of the temperatures, deriving equations for the color coordinates as a function of temperature, calculating the color coordinates and lumen output fractions on-line, and controlling the light output and color of the LEDs based upon the calculated color coordinates and lumen based upon the calculated color coordinates and lumen output fractions. However, the demand on calculation power will increase cost of the lighting system. Further, the color rendering properties of a three-color system may not be satisfactory. Note that the color rendering index can only be optimized by choosing the wavelengths of the LEDs when designing the lighting system. This can be overcome by using more colors. However, the demand on calculation power would then raise even more, and thus the cost. Therefore, there is a need for an improved LED lighting system, and an improved method of controlling such a LED lighting system.